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Polytope of Type {2,20,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,6}*480a
if this polytope has a name.
Group : SmallGroup(480,1088)
Rank : 4
Schlafli Type : {2,20,6}
Number of vertices, edges, etc : 2, 20, 60, 6
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,20,6,2} of size 960
   {2,20,6,3} of size 1440
   {2,20,6,4} of size 1920
   {2,20,6,3} of size 1920
   {2,20,6,4} of size 1920
Vertex Figure Of :
   {2,2,20,6} of size 960
   {3,2,20,6} of size 1440
   {4,2,20,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,10,6}*240
   3-fold quotients : {2,20,2}*160
   5-fold quotients : {2,4,6}*96a
   6-fold quotients : {2,10,2}*80
   10-fold quotients : {2,2,6}*48
   12-fold quotients : {2,5,2}*40
   15-fold quotients : {2,4,2}*32
   20-fold quotients : {2,2,3}*24
   30-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,20,6}*960, {2,40,6}*960, {2,20,12}*960
   3-fold covers : {2,20,18}*1440a, {6,20,6}*1440, {2,60,6}*1440a, {2,60,6}*1440b
   4-fold covers : {4,20,12}*1920, {8,20,6}*1920a, {4,40,6}*1920a, {2,40,12}*1920a, {2,20,24}*1920a, {8,20,6}*1920b, {4,40,6}*1920b, {2,40,12}*1920b, {2,20,24}*1920b, {4,20,6}*1920a, {2,20,12}*1920a, {2,80,6}*1920, {2,20,6}*1920a
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)(25,26)
(29,32)(30,31)(33,48)(34,52)(35,51)(36,50)(37,49)(38,53)(39,57)(40,56)(41,55)
(42,54)(43,58)(44,62)(45,61)(46,60)(47,59);;
s2 := ( 3,34)( 4,33)( 5,37)( 6,36)( 7,35)( 8,44)( 9,43)(10,47)(11,46)(12,45)
(13,39)(14,38)(15,42)(16,41)(17,40)(18,49)(19,48)(20,52)(21,51)(22,50)(23,59)
(24,58)(25,62)(26,61)(27,60)(28,54)(29,53)(30,57)(31,56)(32,55);;
s3 := ( 3, 8)( 4, 9)( 5,10)( 6,11)( 7,12)(18,23)(19,24)(20,25)(21,26)(22,27)
(33,38)(34,39)(35,40)(36,41)(37,42)(48,53)(49,54)(50,55)(51,56)(52,57);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(62)!(1,2);
s1 := Sym(62)!( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)
(25,26)(29,32)(30,31)(33,48)(34,52)(35,51)(36,50)(37,49)(38,53)(39,57)(40,56)
(41,55)(42,54)(43,58)(44,62)(45,61)(46,60)(47,59);
s2 := Sym(62)!( 3,34)( 4,33)( 5,37)( 6,36)( 7,35)( 8,44)( 9,43)(10,47)(11,46)
(12,45)(13,39)(14,38)(15,42)(16,41)(17,40)(18,49)(19,48)(20,52)(21,51)(22,50)
(23,59)(24,58)(25,62)(26,61)(27,60)(28,54)(29,53)(30,57)(31,56)(32,55);
s3 := Sym(62)!( 3, 8)( 4, 9)( 5,10)( 6,11)( 7,12)(18,23)(19,24)(20,25)(21,26)
(22,27)(33,38)(34,39)(35,40)(36,41)(37,42)(48,53)(49,54)(50,55)(51,56)(52,57);
poly := sub<Sym(62)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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